Projection optical system and projection display device

ABSTRACT

A projection optical system consists of, in order from the magnification side, a first optical system, which consists of one convex mirror and a plurality of lenses disposed on the reduction side of the convex mirror, and a second optical system. The lens closest to the magnification side in the first optical system is a negative lens. Assuming that a paraxial radius of curvature of the convex mirror is Mr and a focal length of the negative lens closest to the magnification side in the first optical system is fL1, Conditional Expression is satisfied:
 
0&lt; Mr/fL 1&lt;4.5.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. § 119 toJapanese Patent Application No. 2017-157550, filed on Aug. 17, 2017. Theabove application is hereby expressly incorporated by reference, in itsentirety, into the present application.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a projection optical system and aprojection display device comprising the projection optical system.

2. Description of the Related Art

In the past, projection display devices, each of which projects an imagedisplayed on a light valve such as a liquid crystal display element or aDigital Micromirror Device (DMD: registered trademark) onto a screen orthe like in an enlarged manner, have come into widespread use. In aprojection optical system used in combination with a light valve in aprojection display device, it has been demanded that aberrationcorrection appropriate for the resolution of the light valve issatisfactorily performed in response to recent improvement inperformance of the light valve.

Examples of the projection optical system applicable to known projectiondisplay devices include optical systems described in JP2017-10023A,JP2017-32925A, JP2017-32927A, U.S. Pat. No. 9,335,524B, and JP5484098B.JP2017-10023A, JP2017-32925A, JP2017-32927A, U.S. Pat. No. 9,335,524B,and JP5484098B disclose an optical system that is composed ofcombination of a reflective optical system consisting of a mirrordisposed to be closest to the magnification side and a refractiveoptical system including a plurality of lenses so as to form anintermediate image in the refractive optical system.

SUMMARY OF THE INVENTION

There is a demand for the projection optical system mounted on theprojection display device to have a higher performance while having acompact configuration in consideration of improvement in degree offreedom in setting the distance to the screen and the installability inthe indoor space and to have a wide angle.

However, in each optical system described in JP2017-10023A,JP2017-32925A, JP2017-32927A, and U.S. Pat. No. 9,335,524B, not only themirror is large, but also correction of off-axis aberrations such asdistortion and field curvature is not enough for the recent demand. Inthe optical system described in JP5484098B, not only the mirror islarge, but also wide angle formation and satisfactory aberration are notachieved at the same time.

The present invention has an object to provide a projection opticalsystem that is composed of combination of a reflective optical systemand a refractive optical system so as to form an intermediate image andthat has high optical performance by achieving a wide angle andsatisfactorily correcting various aberrations without enlarging thereflective optical system, and a projection display device comprisingthe projection optical system.

In order to achieve the above-mentioned object, a projection opticalsystem of the present invention consists of, in order from amagnification side to a reduction side: a first optical system thatconsists of one convex mirror and a plurality of lenses disposed on thereduction side of the convex mirror; and a second optical system thatincludes a plurality of lenses. The second optical system forms anintermediate image at a position conjugate to a reduction side imagingsurface, and the first optical system forms a final image, which isconjugate to the intermediate image, on a magnification side imagingsurface. A lens closest to the magnification side in the first opticalsystem is a negative lens. In addition, assuming that a paraxial radiusof curvature of the convex mirror is Mr and a focal length of thenegative lens closest to the magnification side in the first opticalsystem is fL1, Conditional Expression (1) is satisfied.0<Mr/fL1<4.5  (1)

In the projection optical system of the present invention, it ispreferable to satisfy the Conditional Expression (1-1).0.5<Mr/fL1<4  (1-1)

In the projection optical system of the present invention, assuming thata composite focal length of all lenses positioned to be closer to thereduction side than the convex mirror is fR and a focal length of theprojection optical system is f, it is preferable to satisfy theConditional Expression (2), and it is more preferable to satisfy theConditional Expression (2-1).1.5<|fR/f|<3.5  (2)1.6<|fR/f|<2.6  (2-1)

In the projection optical system of the present invention, assuming thata focal length of the first optical system is f1 and a focal length ofthe second optical system is f2, it is preferable to satisfy theConditional Expression (3), and it is more preferable to satisfy theConditional Expression (3-1).0.03<f1/f2<0.25  (3)0.05<f1/f2<0.22  (3-1)

In the projection optical system of the present invention, it ispreferable that a second lens from the magnification side in the firstoptical system is a negative lens.

In the projection optical system of the present invention, assuming thata focal length of an air lens formed of a reduction side lens surface ofthe lens closest to the magnification side in the first optical systemand a magnification side lens surface of the second lens from themagnification side in the first optical system is fA and a focal lengthof the projection optical system is f, it is preferable to satisfy theConditional Expression (4), and it is more preferable to satisfy theConditional Expression (4-1).−8<fA/|f|<−2  (4)−7<fA/|f|<−2.4  (4-1)

In the projection optical system of the present invention, assuming thatan Abbe number of the second lens from the magnification side in thefirst optical system at the d line is νd2, it is preferable to satisfythe Conditional Expression (5), and it is more preferable to satisfy theConditional Expression (5-1).10<νd2<40  (5)15<νd2<35  (5-1)

In the projection optical system of the present invention, assuming thatthe first optical system and the second optical system have a commonoptical axis, an air gap on the optical axis between the first opticalsystem and the second optical system is DG12, and an air gap on theoptical axis between the convex mirror and the lens closest to themagnification side in the first optical system is Dm, it is preferableto satisfy the Conditional Expression (6), and it is more preferable tosatisfy the Conditional Expression (6-1).0.6<DG12/Dm<1.5  (6)0.7<DG12/Dm<1.2  (6-1)

A projection display device of the present invention comprises: a lightsource; a light valve into which light emitted from the light source isincident; and the projection optical system of the present invention. Itis preferable that the projection optical system projects an opticalimage using modulated light, which is modulated through the light valve,onto a screen.

In a case where the projection optical system of the present inventionis applied to a projection display device, the “magnification side”means a projection target side (screen side), the “reduction side” meansan original image display region side (light valve side).

In the present specification, the sign of the refractive power (alsoreferred to as a power) and the surface shape of the optical surfacewill be considered in terms of the paraxial region unless otherwisespecified. Further, the values used in the above conditional expressionsare values in a case where the distance from the magnification sideimaging surface to the lens surface closest to the magnification side isset to be infinite and the d line (a wavelength of 587.6 nm(nanometers)) is set as a reference. The sign of Mr is negative in acase where the reflective surface is convex.

In the present description, it should be noted that the terms“consisting of ˜” and “consists of ˜” are used in a substantial sense,and mean that the imaging lens may include not only the above-mentionedelements but also lenses substantially having no refractive powers,optical elements, which are not lenses, such as a stop, a filter, and acover glass, and mechanism parts such as a lens flange, a lens barrel,an imaging element, and a camera shaking correction mechanism.

According to the present invention, it is possible to provide aprojection optical system that is composed of combination of areflective optical system and a refractive optical system so as to forman intermediate image and that has high optical performance by achievinga wide angle and satisfactorily correcting various aberrations withoutenlarging the reflective optical system, and a projection display devicecomprising the projection optical system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view illustrating a configuration and anoptical path of a projection optical system of Example 1 of the presentinvention.

FIG. 2 is a cross-sectional view illustrating a configuration and anoptical path of a projection optical system of Example 2 of the presentinvention.

FIG. 3 is a cross-sectional view illustrating a configuration and anoptical path of a projection optical system of Example 3 of the presentinvention.

FIG. 4 is a cross-sectional view illustrating a configuration and anoptical path of a projection optical system of Example 4 of the presentinvention.

FIG. 5 is a diagram of aberrations of the projection optical system ofExample 1 of the present invention.

FIG. 6 is a diagram of aberrations of the projection optical system ofExample 2 of the present invention.

FIG. 7 is a diagram of aberrations of the projection optical system ofExample 3 of the present invention.

FIG. 8 is a diagram of aberrations of the projection optical system ofExample 4 of the present invention.

FIG. 9 is a schematic configuration diagram of a projection displaydevice according to an embodiment of the present invention.

FIG. 10 is a schematic configuration diagram of a projection displaydevice according to another embodiment of the present invention.

FIG. 11 is a schematic configuration diagram of a projection displaydevice according to still another embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, embodiments of the present invention will be described withreference to drawings. FIG. 1 is a cross-sectional view illustrating aconfiguration of a projection optical system according to an embodimentof the present invention. The exemplary configuration shown in FIG. 1corresponds to Example 1 to be described later. In FIG. 1, the left sideis the magnification side, and the right side is the reduction side, andrays with the maximum angle of view k1 and rays with a low angle of viewk2 are also shown.

In FIG. 1, assuming that the projection optical system is mounted on aprojection display device, the screen Scr, the optical member PP and theimage display surface Sim of the light valve are also illustrated. Theoptical member PP is a member of which an incident surface and an exitsurface are parallel, and is a member such as a prism, a filter, or acover glass used in the color synthesizing section or the illuminationlight separating section. The optical member PP is not an indispensablecomponent, and the optical member PP may be configured to be omitted.

In a case where the configuration shown in FIG. 1 is applied to theprojection display device, rays, which are made to have imageinformation through the image display surface Sim, are incident into theprojection optical system through the optical member PP, and aretransmitted onto a screen (not shown in the drawing) through theprojection optical system. That is, the image display surface Simcorresponds to the reduction side imaging surface, and the screencorresponds to the magnification side imaging surface.

The projection optical system is an optical system that forms anintermediate image MI at a position conjugate to a reduction sideimaging surface and forms the intermediate image again on amagnification side imaging surface. The projection optical systemconsists of, in order from the magnification side to the reduction side,a first optical system G1, and a second optical system G2. The secondoptical system G2 forms an intermediate image MI at a position conjugateto a reduction side imaging surface, and the first optical system G1forms a final image, which is conjugate to the intermediate image MI, ona magnification side imaging surface. In the example of FIG. 1, theintermediate image MI is positioned between the first optical system G1and the second optical system G2. In FIG. 1, the intermediate image MIis conceptually shown, and a part of the intermediate image MI includingthe vicinity of the optical axis is indicated by the dotted line, and aposition of the intermediate image MI in the direction of the opticalaxis is basically shown as the position in the vicinity of the opticalaxis.

The first optical system G1 consists of one convex mirror M and aplurality of lenses disposed on the reduction side of the convex mirrorM. The convex mirror M is a mirror having a convex reflective surfaceand is disposed to be closest to the magnification side of the wholesystem. The second optical system G2 is configured to include aplurality of lenses. That is, the projection optical system consists ofa reflective optical system and a refractive optical system. Among them,the reflective optical system consists of a convex mirror M, and therefractive optical system comprises all the lenses included in the firstoptical system G1 and all the lenses included in the second opticalsystem 2G.

In the example shown in FIG. 1, the first optical system G1 consists of,in order from the magnification side to the reduction side, a convexmirror M and eight lenses L1 a, L1 b, L1 c, L1 d, L1 e, L1 f, L1 g, andL1 h. The second optical system G2 comprises, in order from themagnification side to the reduction side, only nine lenses L2 a, L2 b,L2 c, L2 d, L2 e, L2 f, L2 g, L2 h, and L2 i as lenses having refractivepowers. An aperture stop St is disposed between the lens L2 e and thelens L2 f. However, the example shown in FIG. 1 is just an example, andthe number of lenses of each of the first optical system G1 and thesecond optical system G2 may be set to be different from that in theexample shown in FIG. 1.

In the projection optical system configured to form the intermediateimage as described above, the back focal length of the first opticalsystem G1 can be shortened, the diameter of the optical element closestto the magnification side in the first optical system G1, that is, themirror diameter in the present embodiment can be reduced, and the focallength of the whole system can be shortened. Thereby, an optical systemsuitable for achieving a wide angle is realized. Further, since a convexmirror is disposed to be closest to the magnification side, it ispossible to correct off-axis rays at a high position without generatinglateral chromatic aberration, and there is an advantage in aberrationcorrection.

The lens L1 a closest to the magnification side in the first opticalsystem G1 is a negative lens. Since the lens L1 a closest to themagnification side is set to be a negative lens, it becomes easy toachieve the wide angle, and there is an advantage in correction ofdistortion.

The second lens L1 b from the magnification side in the first opticalsystem G1 is also preferably a negative lens. Since the second lens L1 bfrom the magnification side is set to be a negative lens, there is anadvantage in correction of off-axis aberration, in particular,correction of astigmatism.

Further, assuming that a paraxial radius of curvature of the convexmirror M is Mr and a focal length of the negative lens closest to themagnification side in the first optical system G1 is fL1, the projectionoptical system is configured to satisfy Conditional Expression (1).Here, the sign of Mr is negative in a case where the reflective surfaceis convex. Since the definition of the sign of Mr is considered and thelens L1 a closest to the magnification side is a negative lens,0<Mr/fL1. Conditional Expression (1) is an expression relating to therelative strength between the power of the convex mirror M and the powerof the lens L1 a closest to the magnification side. By not allowing theresult of Conditional Expression (1) to be equal to or greater than theupper limit, it is possible to prevent the power of the convex mirror Mfrom becoming relatively excessively weak, or it is possible to preventthe power of the lens closest to the magnification side L1 a frombecoming relatively excessively strong. Thereby, it is possible toensure the contribution ratio of the convex mirror M. As a result, itbecomes easy to achieve both a wide angle and a small diameter of theconvex mirror M.0<Mr/fL1<4.5  (1)

Further, it is preferable to satisfy Conditional Expression (1-1). Bynot allowing the result of Conditional Expression (1-1) to be equal toor less than the lower limit, it is possible to prevent the power of theconvex mirror M from becoming relatively excessively strong, or it ispossible to prevent the power of the lens closest to the magnificationside L1 a from becoming relatively excessively weak. Thereby, it ispossible to prevent the load on the convex mirror M from becomingexcessively large. Thus, it becomes easy to correct distortion and fieldcurvature, which is generated by the convex mirror M, with the lenscloser to the reduction side than the convex mirror M.0.5<Mr/fL1<4  (1-1)

In the projection optical system, assuming that a composite focal lengthof all lenses positioned to be closer to the reduction side than theconvex mirror M is fR and a focal length of the projection opticalsystem is f, it is preferable to satisfy the Conditional Expression (2).fR is the composite focal length of the optical members other than theconvex mirror M among the optical members composing the projectionoptical system, and is the focal length of the above-mentionedrefractive optical system. By not allowing the result of ConditionalExpression (2) to be equal to or less than the lower limit, therefractive power of the refractive optical system can be minimized, andthe ratio of contribution of the convex mirror M to the wide angle canbe secured. By not allowing the result of Conditional Expression (2) tobe equal to or greater than the upper limit, the refractive power of therefractive optical system can be ensured, and it becomes easy to correctdistortion, field curvature, and lateral chromatic aberration. Inaddition, in a case of a configuration in which Conditional Expression(2-1) is satisfied instead of Conditional Expression (2), it is possibleto obtain more favorable characteristics.1.5<|fR/f|<3.5  (2)1.6<|fR/f|<2.6  (2-1)

Assuming that a focal length of the first optical system G1 is f1 and afocal length of the second optical system G2 is f2, it is preferable tosatisfy the Conditional Expression (3). By not allowing the result ofConditional Expression (3) to be equal to or less than the lower limit,there is an advantage in keeping balance favorable between the firstoptical system G1 and the second optical system G2. As a result, itbecomes easy to correct spherical aberration, and it is possible tosuppress the increase in diameter of the lens on the intermediate imageMI side in the second optical system G2. By not allowing the result ofConditional Expression (3) to be equal to or greater than the upperlimit, it is possible to prevent the load of the second optical systemG2 caused by the wide angle from becoming excessively large. As aresult, it becomes easy to correct distortion, and it is possible tosuppress the increase in diameter of the lens on the intermediate imageMI side in the first optical system G1. In addition, in a case of aconfiguration in which Conditional Expression (3-1) is satisfied insteadof Conditional Expression (3), it is possible to obtain more favorablecharacteristics.0.03<f1/f2<0.25  (3)0.05<f1/f2<0.22  (3-1)

Assuming that a focal length of an air lens formed of a reduction sidelens surface of the lens L1 a closest to the magnification side in thefirst optical system G1 and a magnification side lens surface of thesecond lens L1 b from the magnification side in the first optical systemG1 is fA and a focal length of the projection optical system is f, it ispreferable to satisfy the Conditional Expression (4). By not allowingthe result of Conditional Expression (4) to be equal to or less than thelower limit, it is possible to prevent the refractive power of the airlens from becoming excessively weak, and it is possible to suppressoccurrence of astigmatism. By not allowing the result of ConditionalExpression (4) to be equal to or greater than the upper limit, it ispossible to prevent the refractive power of the air lens from becomingexcessively strong. Thereby, it is possible to prevent the distancebetween the lens L1 a and the lens L1 b from becoming excessively wide,and it is possible to suppress the increase in diameter of the lens L1a. In addition, in a case of a configuration in which ConditionalExpression (4-1) is satisfied instead of Conditional Expression (4), itis possible to obtain more favorable characteristics.−8<fA/|f|<−2  (4)−7<fA/|f|<−2.4  (4-1)

The focal length of the air lens formed by the reduction side lenssurface of the lens L1 a closest to the magnification side in the firstoptical system G1 and the magnification side lens surface of the secondlens L1 b from the magnification side in the first optical system G1 canbe obtained from the following expression. In the following expression,the refractive index of the lens L1 a at the d-line is Na, therefractive index of the lens L1 b at the d-line is Nb, the paraxialradius of curvature of the reduction side lens surface of the lens L1 ais Ra, the paraxial radius of curvature of the magnification side lenssurface of the lens L1 b is Rb, and the distance on the optical axisbetween the lens L1 a and the lens L1 b is Dab.

$\frac{1}{fA} = {\left\{ {\frac{1 - {Na}}{Rar} + \frac{{Nb} - 1}{Rbf} - \frac{\left( {1 - {Na}} \right) \times \left( {{Nb} - 1} \right) \times {Dab}}{{Rar} \times {Rbf}}} \right\} \times \frac{1}{Nb}}$

Assuming that an Abbe number of the second lens L1 b from themagnification side in the first optical system G1 at the d line is νd2,it is preferable to satisfy the Conditional Expression (5). By selectinga material so as to satisfy Conditional Expression (5), it is possibleto satisfactorily correct lateral chromatic aberration. By not allowingthe result of Conditional Expression (5) to be equal to or less than thelower limit, it becomes easy to configure the lens system whilesuppressing the costs. In a case where the second lens L1 b from themagnification side in the first optical system G1 is a negative lens,satisfying Conditional Expression (5) makes it easier to correct lateralchromatic aberration. In addition, in a case of a configuration in whichConditional Expression (5-1) is satisfied instead of ConditionalExpression (5), it is possible to obtain more favorable characteristics.10<νd2<40  (5)15<νd2<35  (5-1)

In this projection optical system, it is preferable that the firstoptical system G1 and the second optical system G2 have a common opticalaxis Z. That is, all of the convex mirror M, all the lenses included inthe first optical system G1, and all the lenses included in the secondoptical system G2 preferably have a common optical axis Z. Since thefirst optical system G1 and the second optical system G2 including theconvex mirror M have the common optical axis Z, the structure of theentire projection optical system can be simplified, and thisconfiguration contributes to cost reduction. It should be noted that thecommon optical axis described herein also includes a substantiallycommon optical axis. For example, the common optical axis includes aproduction tolerance range which does not significantly degrade theperformance of the optical system.

In a case where the first optical system G1 and the second opticalsystem G2 have the common optical axis Z, assuming that an air gap onthe optical axis Z between the first optical system G1 and the secondoptical system G2 is DG12 and an air gap on the optical axis Z betweenthe convex mirror M and the lens L1 a closest to the magnification sidein the first optical system G1 is Dm, it is preferable to satisfy theConditional Expression (6). By not allowing the result of ConditionalExpression (6) to be equal to or less than the lower limit, the air gapbetween the convex mirror M and the lens L1 a closest to themagnification side in the first optical system G1 can be prevented frombecoming excessively large. As a result, it is possible to suppress theincrease in size of convex mirror M. By not allowing the result ofConditional Expression (6) to be equal to or less than the lower limit,it is possible to prevent the air gap between the first optical systemG1 and the second optical system G2 from becoming excessively small, andit is possible to adopt a configuration in which no lens is disposed inthe vicinity of the intermediate image MI. Thus, it is possible toprevent reflection of scratches or the like on the final image. By notallowing the result of Conditional Expression (6) to be equal to orgreater than the upper limit, the length of the air gap between thefirst optical system G1 and the second optical system G2 can beminimized, and the total length of the lens system can be minimized. Inaddition, in a case of a configuration in which Conditional Expression(6-1) is satisfied instead of Conditional Expression (6), it is possibleto obtain more favorable characteristics.0.6<DG12/Dm<1.5  (6)0.7<DG12/Dm<1.2  (6-1)

The above-mentioned preferred configurations and availableconfigurations may be arbitrary combinations, and it is preferable toselectively adopt the configurations in accordance with requiredspecification. According to the present embodiment, it is possible torealize a projection optical system that has a mirror and a plurality oflenses so as to form an intermediate image and maintains high opticalperformance by achieving a wide angle and satisfactorily correctingvarious aberrations without increasing the size of the mirror. The term“wide angle” described herein means that the total angle of view isgreater than 130 degrees.

Next, numerical examples of the projection optical system of the presentinvention will be described. It should be noted that the numerical datapieces of the following examples are all normalized such that theabsolute value of the focal length of the whole system is 1.00, and arerounded up to a predetermined number of decimal places.

Example 1

A lens configuration and an optical path of a projection optical systemof Example 1 are shown in FIG. 1, and a configuration and anillustration method thereof is as described above. Therefore, repeateddescriptions are partially omitted herein. The projection optical systemof Example 1 consists of, in order from the magnification side, a firstoptical system G1 and a second optical system G2. The first opticalsystem G1 consists of, in order from the magnification side, a convexmirror M and eight lenses L1 a to L1 h. The second optical system G2consists of, in order from the magnification side, five lenses L2 a toL2 e, an aperture stop St, and four lenses L2 f to L2 i.

Table 1 shows basic lens data of the projection optical system ofExample 1, Table 2 shows specification, and Table 3 shows asphericsurface coefficients thereof. In Table 1, the column of the surfacenumber shows surface numbers. The surface closest to the magnificationside is the first surface, and the surface numbers increase one by onetoward the reduction side. The column of R shows radii of curvature ofthe respective surfaces. The column of D shows surface distances on theoptical axis between the respective surfaces and the surfaces adjacentto the reduction side. Further, the column of Nd shows refractiveindexes of the respective components at the d line (a wavelength of587.6 nm (nanometers)), and the column of νd shows Abbe numbers of therespective components at the d line.

In Table 1, reference signs of radii of curvature of surface shapesconvex toward the magnification side are set to be positive, andreference signs of radii of curvature of surface shapes convex towardthe reduction side are set to be negative. Table 1 additionally showsthe aperture stop St and the optical member PP. In Table 1, the“reflective surface” is noted in the column of Nd of the surfacecorresponding to the convex mirror M, and the surface number and thephrase (St) are noted in the column of the surface number of the surfacecorresponding to the aperture stop St. The numerical value in theuppermost place in the column of D in Table 1 corresponds to thedistance from the magnification side imaging surface to the convexmirror M.

Table 2 shows, as specification of the projection optical system,respective values of the absolute value |f| of the focal length, theback focal length Bf at the air conversion distance in a case where thereduction side is set as a back side, F number FNo., and the maximumtotal angle of view 2ω, on the basis of the d line. [°] in the place of2ω indicates that the unit thereof is a degree.

In Table 1, the reference sign * is attached to surface numbers ofaspheric surfaces, and numerical values of the paraxial radius ofcurvature are written into the column of the radius of curvature of theaspheric surface. Table 3 shows surface numbers of the asphericsurfaces, and aspheric surface coefficients of the respective asphericsurfaces. The “E±n” (n: an integer) in numerical values of the asphericsurface coefficients of Table 3 indicates “×10^(±n)”. The asphericsurface coefficients are values of the coefficients KA and Am (m=3, 4,5, . . . , 20) in aspheric surface expression represented as thefollowing expression.Zd=C×h ²/{1+(1−KA×C ² ×h ²)^(1/2) }+ΣAm×h ^(m)

Here, Zd is an aspheric surface depth (a length of a perpendicular froma point on an aspheric surface at height h to a plane that isperpendicular to the optical axis and contacts with the vertex of theaspheric surface),

h is a height (a distance from the optical axis to the lens surface),

C is a paraxial curvature,

KA and Am are aspheric surface coefficients, and

Σ in the aspheric surface expression means the sum with respect to m.

TABLE 1 Example 1 Surface Number R D Nd νd −127.096 *1 −19.4964 4.5505Reflective Surface *2 41.3373 0.6538 1.53158 55.08 *3 3.3397 4.6797 4−2.9832 3.6313 1.80518 25.42 5 −7.1597 0.4994 6 25.9719 2.1383 1.8928620.36 7 −8.7961 0.9493 8 12.1924 1.9662 1.65160 58.55 9 −5.7704 0.45601.84666 23.78 10 5.1477 2.6631 1.53775 74.70 11 −7.3726 1.8049 *12−4.9313 0.9909 1.51007 56.24 *13 −4.1793 3.3856 14 7.1720 2.2312 1.8000029.84 15 115.9821 3.8185 16 −5.2549 0.5446 1.58913 61.13 17 7.81302.4791 18 51.4570 2.3199 1.77250 49.60 19 −7.2478 5.9148 20 7.56322.0950 1.78800 47.32 21 −6.9690 0.3337 1.84666 23.78 22 −46.6481 1.930623 2.4901 0.6822 1.80518 25.42 24 1.8379 0.8267 25(St) ∞ 1.3760 26−2.2231 0.7962 1.62588 35.70 27 7.9627 1.3216 1.49700 81.61 28 −4.01390.1053 29 −92.7904 1.7392 1.49700 81.61 30 −4.0283 0.2435 31 9.58450.9962 1.72916 54.68 32 −152.3456 2.7026 33 ∞ 5.8646 1.51633 64.14 34 ∞

TABLE 2 Example 1 |f| 1.00 Bf 6.57 FNo. 2.00 2ω[°] 138.8

TABLE 3 Example 1 Surface Number 1 2 3 KA 3.531517823033E−01 1.077727987217E+02  1.089666076850E+00 A3 1.501030404624E−03−1.327765671580E−01 −1.131913510215E−01 A4 −9.768646107915E−04  3.691811030265E−01  3.525223913580E−01 A5 3.361988060752E−05−2.401787218822E−01 −1.791109324330E−01 A6 5.477662417900E−05 4.562025809181E−03 −1.165803153364E−01 A7 −5.240918419781E−06  7.050492972831E−02  1.579114897989E−01 A8 −1.229918705327E−06 −2.425592962243E−02 −1.948030697406E−02 A9 1.774015200670E−07−8.767850018532E−03 −4.266429793852E−02 A10 1.321446959589E−08 6.369154908479E−03  1.312795776927E−02 A11 −2.939507476279E−09 −6.997837199031E−06  6.883554193968E−03 A12 −4.888399941398E−11 −7.451091518193E−04 −2.994717431046E−03 A13 2.770384946950E−11 1.138175774985E−04 −6.496764146345E−04 A14 −3.497668158758E−13  4.189962500117E−05  3.631324101141E−04 A15 −1.514847884985E−13 −1.199552949259E−05  3.636598191804E−05 A16 4.557796049357E−15−7.593482102834E−07 −2.548276552361E−05 A17 4.480740506852E−16 5.225606853583E−07 −1.062749726204E−06 A18 −1.863726845198E−17 −2.294805043587E−08  9.609789941744E−07 A19 −5.550148460603E−19 −8.564793616683E−09  1.272047581428E−08 A20 2.759145250815E−20 8.532013360197E−10 −1.520987579422E−08 Surface Number 12 13 KA 1.000000000000E+00  1.000000000000E+00 A3 −2.227492911325E−03−2.538013673743E−03 A4  4.063876592790E−03  1.091035753319E−02 A5 1.809673199911E−02  5.418878143466E−03 A6 −1.230988827127E−02−1.687216398111E−03 A7 −3.776167347919E−03 −3.002681191533E−03 A8 5.939568396606E−03  1.140765516621E−03 A9 −4.744229716872E−04 8.523916935080E−04 A10 −1.321466503168E−03 −5.103860653863E−04 A11 3.503591891641E−04 −5.793545428653E−05 A12  1.404436555611E−04 8.614487714219E−05 A13 −6.185277953832E−05 −6.794921015464E−06 A14−5.810197796232E−06 −6.773547736541E−06 A15  5.259712360923E−06 1.287045865290E−06 A16 −1.462856178957E−07  2.233404545603E−07 A17−2.224591683839E−07 −7.335655212592E−08 A18  2.063563759948E−08−3.966046920239E−11 A19  3.754854257202E−09  1.466292871897E−09 A20−4.986968961128E−10 −1.112789844347E−10

FIG. 5 shows aberration diagrams of spherical aberration, astigmatism,distortion, and lateral chromatic aberration of the projection opticalsystem of Example 1 in order from the left side. In the sphericalaberration diagram, aberrations at the d line (a wavelength of 587.6nm), the C line (a wavelength of 656.3 nm), and the F line (a wavelengthof 486.1 nm) are respectively indicated by the solid line, the longdashed line, and the short dashed line. In the astigmatism diagram,aberration in the sagittal direction at the d line is indicated by thesolid line, and aberration in the tangential direction at the d line isindicated by the short dashed line. In the distortion diagram,aberration at the d line is indicated by the solid line. In the lateralchromatic aberration diagram, aberrations at the C line and the F lineare respectively indicated by the long dashed line and the short dashedline. In the spherical aberration diagram, FNo. indicates an F number.In the other aberration diagrams, co indicates a half angle of view. Theaberration diagrams are diagrams in a case where the distance from themagnification side imaging surface to the convex mirror M is a valueshown in Table 1.

In the description of Example 1, reference signs, meanings, anddescription methods of the respective data pieces are the same as thosein the following examples unless otherwise noted. Therefore, in thefollowing description, repeated description will be omitted.

Example 2

FIG. 2 is a cross-sectional view of a lens configuration and an opticalpath of a projection optical system of Example 2. The projection opticalsystem of Example 2 consists of, in order from the magnification side, afirst optical system G1 and a second optical system G2. The firstoptical system G1 consists of, in order from the magnification side, aconvex mirror M and eight lenses L1 a to L1 h. The second optical systemG2 consists of, in order from the magnification side, five lenses L2 ato L2 e, an aperture stop St, and four lenses L2 f to L2 i.

Table 4 shows basic lens data of the projection optical system ofExample 2, Table 5 shows specification, Table 6 shows aspheric surfacecoefficients, and FIG. 6 shows aberration diagrams. The aberrationdiagrams are diagrams in a case where the distance from themagnification side imaging surface to the convex mirror M is a valueshown in Table 4.

TABLE 4 Example 2 Surface Number R D Nd νd −127.201 *1 −20.397 4.3087Reflective Surface *2 42.4875 0.6542 1.53158 55.08 *3 2.7105 4.0918 4−3.0187 3.1930 1.75520 27.51 5 −7.1712 0.7684 6 23.4501 2.1806 1.8928620.36 7 −8.8576 1.2928 8 11.3669 1.9481 1.65160 58.55 9 −5.6287 0.24521.84666 23.78 10 5.1213 2.5890 1.53775 74.70 11 −7.7706 1.6028 *12−5.4179 0.7847 1.51007 56.24 *13 −4.1515 3.3592 14 7.5923 2.5191 1.8010034.97 15 315.2503 3.8407 16 −5.4932 0.4326 1.58267 46.42 17 7.88382.4610 18 42.5278 2.2898 1.78800 47.37 19 −7.7059 5.6796 20 8.41412.1420 1.80400 46.58 21 −6.9473 0.2542 1.84666 23.78 22 −48.9831 2.458023 2.4540 0.4287 1.69895 30.13 24 1.9513 1.0052 25(St) ∞ 1.3996 26−2.4222 0.9599 1.59551 39.24 27 8.3222 1.3047 1.49700 81.61 28 −4.48390.0660 29 −85.3914 1.4995 1.49700 81.61 30 −4.1432 1.3628 31 8.71651.0317 1.69680 55.53 32 232.6726 2.3805 33 ∞ 5.8694 1.51633 64.14 34 ∞

TABLE 5 Example 2 |f| 1.00 Bf 6.45 FNo. 2.00 2ω[°] 138.9

TABLE 6 Example 2 Surface Number 1 2 3 KA 4.537514111053E−01 1.257784966106E+02  8.260569596242E−01 A3 1.110299279673E−03−1.243051350350E−01 −1.347031859684E−01 A4 −9.853125147234E−04  4.114883950985E−01  4.719930934516E−01 A5 5.340623949575E−05−2.932957431451E−01 −2.759131366671E−01 A6 5.554493334923E−05 1.270257471454E−02 −1.801839195316E−01 A7 −5.936735189476E−06  9.089852238351E−02  2.772749437989E−01 A8 −1.247918043068E−06 −3.422172060134E−02 −3.818646733702E−02 A9 1.940741592492E−07−1.186406076485E−02 −8.709405843660E−02 A10 1.325503230163E−08 9.442086366085E−03  2.887991910981E−02 A11 −3.196297099607E−09 −9.131074895250E−05  1.635712007709E−02 A12 −4.433900782206E−11 −1.179309930794E−03 −7.638294318489E−03 A13 3.017604344768E−11 1.936242277300E−04 −1.798070643150E−03 A14 −4.303276651765E−13  7.102661860693E−05  1.079032031457E−03 A15 −1.657942160189E−13 −2.153612499748E−05  1.171672260454E−04 A16 5.177883363366E−15−1.371378013999E−06 −8.839117425316E−05 A17 4.934684770072E−16 1.003473934124E−06 −3.979390911246E−06 A18 −2.096055566634E−17 −4.572518925574E−08  3.895093433468E−06 A19 −6.155439310878E−19 −1.765308217186E−08  5.517685381523E−08 A20 3.104398731658E−20 1.814261384300E−09 −7.208734111971E−08 Surface Number 12 13 KA1.000000000000E+00  1.000000000000E+00 A3 1.120338685336E−03−4.157832073960E−03 A4 −5.108574792890E−03   1.195520896409E−02 A52.502754962011E−02  5.292791560705E−03 A6 −1.148003884383E−02 −1.762135069895E−03 A7 −8.013070525196E−03  −3.134044758392E−03 A87.190622966439E−03  1.011467238451E−03 A9 4.966059196243E−04 9.947809154677E−04 A10 −1.853633733967E−03  −4.804289257095E−04 A112.737683818921E−04 −9.954191921214E−05 A12 2.313114612633E−04 8.513764158623E−05 A13 −6.638935184335E−05  −9.167633544722E−07 A14−1.345975636091E−05  −7.152599990976E−06 A15 6.480284965266E−06 8.427115834461E−07 A16 1.409148117761E−07  2.751565385210E−07 A17−3.008457285498E−07  −5.606206842954E−08 A18 1.919538759353E−08−2.649196235972E−09 A19 5.474052183971E−09  1.193725020449E−09 A20−6.206471619978E−10  −6.352358997404E−11

Example 3

FIG. 3 is a cross-sectional view of a lens configuration and an opticalpath of a projection optical system of Example 3. The projection opticalsystem of Example 3 consists of, in order from the magnification side, afirst optical system G1 and a second optical system G2. The firstoptical system G1 consists of, in order from the magnification side, aconvex mirror M and eight lenses L1 a to L1 h. The second optical systemG2 consists of, in order from the magnification side, five lenses L2 ato L2 e, an aperture stop St, and four lenses L2 f to L2 i. In theexample of FIG. 3, two members, of which the incident surface and theexit surface are parallel, are collectively shown as the optical memberPP.

Table 7 shows basic lens data of the projection optical system ofExample 3, Table 8 shows specification, Table 9 shows aspheric surfacecoefficients, and FIG. 7 shows aberration diagrams. The aberrationdiagrams are diagrams in a case where the distance from themagnification side imaging surface to the convex mirror M is a valueshown in Table 7.

TABLE 7 Example 3 Surface Number R D Nd νd −78.8477 *1 −16.867 5.2837Reflective Surface *2 30.9222 1.1083 1.58313 59.38 *3 4.2268 3.7952 4−3.2096 2.4964 1.80518 25.42 5 −7.4923 0.0985 6 29.8298 1.7026 1.8928620.36 7 −6.9028 0.9736 8 11.7988 2.3626 1.65160 58.55 9 −4.6934 0.49231.84666 23.78 10 5.3549 2.8263 1.49700 81.61 11 −7.5693 0.9253 *12−9.7173 1.6365 1.58313 59.38 *13 −4.2659 0.4504 14 6.2569 4.0893 1.8040046.58 15 11.6497 4.4930 16 −3.7886 0.4933 1.51742 52.43 17 8.7425 0.913218 19.0509 2.3539 1.80610 40.93 19 −6.7866 5.6993 20 6.4165 2.56751.71299 53.87 21 −6.0587 0.4924 1.80518 25.42 22 −27.1071 0.0989 233.6005 1.0973 1.80518 25.42 24 2.2958 1.7880 25(St) ∞ 1.3642 26 −2.38441.2793 1.58144 40.75 27 8.4711 2.0169 1.49700 81.61 28 −5.0720 0.1891 29−56.4439 2.1449 1.49700 81.61 30 −5.5143 0.0981 31 17.1658 1.34771.69680 55.53 32 −29.2382 1.9776 33 ∞ 9.1168 1.63854 55.38 34 ∞ 2.710035 ∞ 0.5421 1.51633 64.14 36 ∞

TABLE 8 Example 3 |f| 1.00 Bf 10.61 FNo. 2.40 2ω[°] 139.2

TABLE 9 Example 3 Surface Number 1 2 3 KA  2.160802527306E−01 6.068219811528E+01  1.774078539976E+00 A3  4.341827903599E−03−1.448721493606E−01 −7.697570427311E−02 A4 −1.829245755840E−03 3.070782880551E−01  1.936088027004E−01 A5 −1.291047286874E−05−1.983910595424E−01 −7.932414977756E−02 A6  1.108859251771E−04 1.649437721294E−02 −6.428465945657E−02 A7 −9.059506643476E−06 4.938781697419E−02  6.550390327333E−02 A8 −2.770978406720E−06−2.217626852854E−02 −7.221613674720E−03 A9  3.797627075358E−07−4.051027313216E−03 −1.327783321600E−02 A10  3.343033968177E−08 5.107500163568E−03  4.165614362747E−03 A11 −7.203245123049E−09−5.098474964263E−04  1.657350331830E−03 A12 −1.442935805614E−10−5.317671236562E−04 −8.248801547510E−04 A13  7.608539342743E−11 1.346820338054E−04 −1.146696454587E−04 A14 −9.689331735534E−13 2.460226029956E−05  8.738794303282E−05 A15 −4.617426506421E−13−1.152511790587E−05  4.408054060731E−06 A16  1.471346529729E−14−8.326763004966E−08 −5.494714354024E−06 A17  1.507608577485E−15 4.548064934599E−07 −6.183360681180E−08 A18 −6.686449212043E−17−3.218664540818E−08  1.874145465048E−07 A19 −2.054527134787E−18−6.973892844299E−09 −1.321411156651E−10 A20  1.092036209438E−19 8.035053473472E−10 −2.709775444746E−09 Surface Number 12 13 KA1.000000000000E+00 1.000000000000E+00 A3 −7.923224850804E−04 −3.985657349698E−03  A4 8.190537671986E−03 1.409362867373E−02 A58.802561671514E−03 3.267858713514E−03 A6 −1.083210502923E−02 −3.398564997080E−03  A7 4.358224198836E−04 −1.333441075447E−03  A83.730254459053E−03 1.297132822934E−03 A9 −1.093864540618E−03 3.150184250885E−04 A10 −6.116416428856E−04  −4.168073200925E−04  A113.076676556809E−04 1.616408750062E−05 A12 4.066780053954E−056.042814559549E−05 A13 −4.003875885346E−05  −1.068100965984E−05  A146.335355074396E−07 −4.103857547122E−06  A15 2.784058043497E−061.207474988208E−06 A16 −2.528089070731E−07  1.001968761220E−07 A17−1.000128015505E−07  −5.766780300067E−08  A18 1.359908471247E−081.711710800980E−09 A19 1.460493843190E−09 1.032034687061E−09 A20−2.427573579640E−10  −9.122421200689E−11 

Example 4

FIG. 4 is a cross-sectional view of a lens configuration and an opticalpath of a projection optical system of Example 4. The projection opticalsystem of Example 4 consists of, in order from the magnification side, afirst optical system G1 and a second optical system G2. The firstoptical system G1 consists of, in order from the magnification side, aconvex mirror M and eight lenses L1 a to L1 h. The second optical systemG2 consists of, in order from the magnification side, five lenses L2 ato L2 e, an aperture stop St, and four lenses L2 f to L2 i. In theexample of FIG. 4, two members, of which the incident surface and theexit surface are parallel, are collectively shown as the optical memberPP.

Table 10 shows basic lens data of the projection optical system ofExample 4, Table 11 shows specification, Table 12 shows aspheric surfacecoefficients, and FIG. 8 shows aberration diagrams. The aberrationdiagrams are diagrams in a case where the distance from themagnification side imaging surface to the convex mirror M is a valueshown in Table 10.

TABLE 10 Example 4 Surface Number R D Nd νd −77.4137 *1 −19.7173 7.983Reflective Surface *2 40.9716 1.1382 1.58313 59.38 *3 9.3012 5.8372 4−4.2473 2.5147 1.89286 20.36 5 −7.4152 0.1186 6 42.8143 2.2778 1.8928620.36 7 −8.5893 0.1189 8 18.8217 3.0254 1.65160 58.55 9 −5.8865 0.59551.84666 23.78 10 6.5705 3.8415 1.53775 74.70 11 −8.7206 0.5438 *12−17.8497 2.0647 1.58313 59.38 *13 −5.1432 0.1473 14 8.7379 3.55731.80400 46.58 15 24.3936 7.6052 16 −11.7304 0.5950 1.80000 29.84 1710.6061 1.0493 18 20.7834 2.8765 1.80518 25.42 19 −9.1426 7.1626 208.4063 3.9094 1.71299 53.87 21 −7.2536 0.5958 1.84666 23.78 22 −21.65810.1186 23 5.5623 1.7736 1.80518 25.42 24 2.8802 1.8497 25(St) ∞ 2.198126 −2.5954 0.6010 1.59551 39.24 27 13.3039 2.4164 1.49700 81.61 28−4.7773 0.1515 29 −37.4835 2.3560 1.49700 81.61 30 −6.1106 0.1186 3125.6485 1.8049 1.65844 50.88 32 −19.0039 2.3854 33 ∞ 11.0166 1.6385455.38 34 ∞ 3.2800 35 ∞ 0.6550 1.51633 64.14 36 ∞

TABLE 11 Example 4 |f| 1.00 Bf 12.82 FNo. 2.40 2ω[°] 145.7

TABLE 12 Example 4 Surface Number 1 2 3 KA 2.592195428275E−01 6.591135878757E+01  2.093120656079E+00 A3 3.954111196549E−03−7.834139720730E−02 −6.679871842875E−05 A4 −1.104760798732E−03  1.418443989809E−01  4.215209721566E−02 A5 −5.906716535808E−05 −7.330836121137E−02 −1.696239038232E−02 A6 4.523853620089E−05 4.358820945654E−03 −5.709095702911E−03 A7 −1.446524041510E−06  1.137233023413E−02  4.715706855226E−03 A8 −8.022042059205E−07 −3.825873880664E−03 −3.472439694971E−04 A9 5.935954723455E−08−6.134846136569E−04 −4.037179044984E−04 A10 7.357336786216E−09 5.463081313490E−04  7.593518591382E−05 A11 −8.361896347412E−10 −3.715767069055E−05  2.155092877919E−05 A12 −3.286947041775E−11 −3.526431239469E−05 −6.237350171478E−06 A13 6.245187793416E−12 6.621812784103E−06 −6.516139330919E−07 A14 2.274507336361E−14 1.022823252410E−06  2.782433373363E−07 A15 −2.634860406576E−14 −3.540332936903E−07  1.115767346556E−08 A16 4.166540347063E−16−3.320039086225E−09 −7.415517240424E−09 A17 5.935737320698E−17 8.642929837558E−09 −7.807451652548E−11 A18 −1.658515558774E−18 −4.639186187888E−10  1.076607206250E−10 A19 −5.559912798904E−20 −8.172315615454E−11  6.125316073998E−14 A20 2.010560883813E−21 7.295616964994E−12 −6.644683083853E−13 Surface Number 12 13 KA1.000000000000E+00 1.000000000000E+00 A3 5.011176439366E−03−2.990121990373E−03  A4 6.213759850542E−03 1.726187951844E−02 A51.680762023462E−03 7.128562275390E−04 A6 −3.895361432686E−03 −3.565089264206E−03  A7 6.419782376500E−04 1.751987881350E−04 A88.078785486065E−04 6.822050195816E−04 A9 −2.778624259855E−04 −6.702878185372E−05  A10 −7.995960268603E−05  −1.046015286267E−04  A114.382626029730E−05 1.860172210602E−05 A12 2.722459148703E−068.696311911985E−06 A13 −3.523222026288E−06  −2.221078046474E−06  A141.171710925451E−07 −3.475866834157E−07  A15 1.555660168374E−071.307643467434E−07 A16 −1.328962113959E−08  3.655832904917E−09 A17−3.590070265306E−09  −3.794385496976E−09  A18 4.242378584183E−101.481097791155E−10 A19 3.387940724366E−11 4.351524808198E−11 A20−4.766172417557E−12  −3.442120342905E−12 

Table 13 shows values corresponding to Conditional Expressions (1) to(6) of the projection optical systems of Examples 1 to 4. In Examples 1to 4, the d line is set as the reference wavelength, and the valuesshown in Table 13 are based on the d line.

TABLE 13 Exam- Exam- Exam- Exam- Expression Number ple 1 ple 2 ple 3 ple4 (1) Mr/fL1 2.84 3.72 1.98 0.94 (2) |fR/f| 1.82 1.72 2.09 2.45 (3)f1/f2 0.18 0.16 0.09 0.08 (4) fA/|f| −2.86 −2.71 −3.47 −5.41 (5) νd225.43 27.51 25.43 20.36 (6) DG12/Dm 0.84 0.89 0.85 0.95

As can be seen from the above data, in each projection optical system ofExamples 1 to 4, the increase in size of the convex mirror M issuppressed, the wide angle is achieved such that the total angle of viewis equal to or greater than 138°, and the F number is 2.4. Thereby,various aberrations are satisfactorily corrected, and high opticalperformance is achieved.

Next, a projection display device according to an embodiment of thepresent invention will be described. FIG. 9 is a schematic configurationdiagram of the projection display device according to theabove-mentioned embodiment of the present invention. The projectiondisplay device 100 shown in FIG. 9 has a projection optical system 10according to the embodiment of the present invention, a light source 15,transmissive display elements 11 a to 11 c as light valves correspondingto respective color light rays, dichroic mirrors 12 and 13 for colorseparation, a cross dichroic prism 14 for color synthesis, condenserlenses 16 a to 16 c, and total reflection mirrors 18 a to 18 c fordeflecting the optical path. In FIG. 9, the projection optical system 10is schematically illustrated. Further, an integrator is disposed betweenthe light source 15 and the dichroic mirror 12, but illustration thereofis omitted in FIG. 9.

White light originated from the light source 15 is separated into rayswith three colors (green light, blue light, red light) through thedichroic mirrors 12 and 13. Thereafter, the rays respectively passthrough the condenser lenses 16 a to 16 c, are incident into andmodulated through the transmissive display elements 11 a to 11 crespectively corresponding to the rays with the respective colors, aresubjected to color synthesis through the cross dichroic prism 14, andare subsequently incident into the projection optical system 10. Theprojection optical system 10 projects an optical image, which is formedby the modulated light modulated through the transmissive displayelements 11 a to 11 c, onto a screen 105.

FIG. 10 is a schematic configuration diagram of a projection displaydevice according to another embodiment of the present invention. Theprojection display device 200 shown in FIG. 10 has a projection opticalsystem 210 according to the embodiment of the present invention, a lightsource 215, DMD elements 21 a to 21 c as light valves corresponding torespective color light beams, total internal reflection (TIR) prisms 24a to 24 c for color separation and color synthesis, and a polarizationseparating prism 25 that separates illumination light and projectionlight. In FIG. 10, the projection optical system 210 is schematicallyillustrated. Further, an integrator is disposed between the light source215 and the polarization separating prism 25, but illustration thereofis omitted in FIG. 10.

White light originated from the light source 215 is reflected on areflective surface inside the polarization separating prism 25, and isseparated into rays with three colors (green light, blue light, redlight) through the TIR prisms 24 a to 24 c. The separated rays with therespective colors are respectively incident into and modulated throughthe corresponding DMD elements 21 a to 21 c, travel through the TIRprisms 24 a to 24 c again in a reverse direction, are subjected to colorsynthesis, are subsequently transmitted through the polarizationseparating prism 25, and are incident into the projection optical system210. The projection optical system 210 projects an optical image, whichis formed by the modulated light modulated through the DMD elements 21 ato 21 c, onto a screen 205.

FIG. 11 is a schematic configuration diagram of a projection displaydevice according to still another embodiment of the present invention.The projection display device 300 shown in FIG. 11 has a projectionoptical system 310 according to the embodiment of the present invention,a light source 315, reflective display elements 31 a to 31 c as lightvalves corresponding to respective color light beams, dichroic mirrors32 and 33 for color separation, a cross dichroic prism 34 for colorsynthesis, a total reflection mirror 38 for deflecting the optical path,and polarization separating prisms 35 a to 35 c. In FIG. 11, theprojection optical system 310 is schematically illustrated. Further, anintegrator is disposed between the light source 315 and the dichroicmirror 32, but illustration thereof is omitted in FIG. 11.

White light originated from the light source 315 is separated into rayswith three colors (green light, blue light, red light) through thedichroic mirrors 32 and 33. The separated rays with the respectivecolors respectively pass through the polarization separating prisms 35 ato 35 c, are incident into and modulated through the reflective displayelements 31 a to 31 c respectively corresponding to the rays with therespective colors, are subjected to color synthesis through the crossdichroic prism 34, and are subsequently incident into the projectionoptical system 310. The projection optical system 310 projects anoptical image, which is formed by the modulated light modulated throughthe reflective display elements 31 a to 31 c, onto a screen 305.

The present invention has been hitherto described through embodimentsand examples, but the present invention is not limited to theabove-mentioned embodiments and examples, and may be modified intovarious forms. For example, values such as the radius of curvature, thesurface distance, the refractive index, the Abbe number, and theaspheric surface coefficient of each lens are not limited to the valuesshown in the numerical examples, and different values may be usedtherefor.

The projection display device of the present invention is also notlimited to the above-mentioned configuration, and various modificationsof the optical member and the light valve used for the ray separation orthe ray synthesis, for example, can be made.

What is claimed is:
 1. A projection optical system consisting of, inorder from a magnification side to a reduction side: a first opticalsystem that consists of one convex mirror and a plurality of lensesdisposed on the reduction side of the convex mirror; and a secondoptical system that includes a plurality of lenses, wherein the secondoptical system forms an intermediate image at a position conjugate to areduction side imaging surface, and the first optical system forms afinal image, which is conjugate to the intermediate image, on amagnification side imaging surface, wherein a lens closest to themagnification side in the first optical system is a negative lens,wherein assuming that a paraxial radius of curvature of the convexmirror is Mr and a focal length of the negative lens closest to themagnification side in the first optical system is fL1, ConditionalExpression (1) is satisfied,0<Mr/fL1<4.5  (1), and wherein assuming that a composite focal length ofall lenses positioned to be closer to the reduction side than the convexmirror is fR and a focal length of the projection optical system is f,Conditional Expression (2) is satisfied,1.5<|fR/f|<3.5  (2).
 2. The projection optical system according to claim1, wherein a second lens from the magnification side in the firstoptical system is a negative lens.
 3. The projection optical systemaccording to claim 1, wherein assuming that a focal length of an airlens formed of a reduction side lens surface of the lens closest to themagnification side in the first optical system and a magnification sidelens surface of the second lens from the magnification side in the firstoptical system is fA and a focal length of the projection optical systemis f, Conditional Expression (4) is satisfied,−8<fA/|f|<−2  (4).
 4. The projection optical system according to claim3, wherein Conditional Expression (4-1) is satisfied,−7<fA/|f|<−2.4  (4-1).
 5. The projection optical system according toclaim 1, wherein assuming that the first optical system and the secondoptical system have a common optical axis, an air gap on the opticalaxis between the first optical system and the second optical system isDG12, and an air gap on the optical axis between the convex mirror andthe lens closest to the magnification side in the first optical systemis Dm, Conditional Expression (6) is satisfied,0.6<DG12/Dm<1.5  (6).
 6. The projection optical system according toclaim 5, wherein Conditional Expression (6-1) is satisfied,0.7<DG12/Dm<1.2  (6-1).
 7. The projection optical system according toclaim 1, wherein Conditional Expression (1-1) is satisfied,0.5<Mr/fL1<4  (1-1).
 8. The projection optical system according to claim1, wherein Conditional Expression (2-1) is satisfied,1.6<|fR/f|<2.6  (2-1).
 9. A projection display device comprising: alight source; a light valve into which light emitted from the lightsource is incident; and the projection optical system according to claim1, wherein the projection optical system projects an optical image usingmodulated light, which is modulated through the light valve, onto ascreen.
 10. A projection optical system consisting of, in order from amagnification side to a reduction side: a first optical system thatconsists of one convex mirror and a plurality of lenses disposed on thereduction side of the convex mirror; and a second optical system thatincludes a plurality of lenses, wherein the second optical system formsan intermediate image at a position conjugate to a reduction sideimaging surface, and the first optical system forms a final image, whichis conjugate to the intermediate image, on a magnification side imagingsurface, wherein a lens closest to the magnification side in the firstoptical system is a negative lens, wherein assuming that a paraxialradius of curvature of the convex mirror is Mr and a focal length of thenegative lens closest to the magnification side in the first opticalsystem is fL1, Conditional Expression (1) is satisfied,0<Mr/fL1<4.5  (1), and wherein assuming that a focal length of the firstoptical system is f1 and a focal length of the second optical system isf2, Conditional Expression (3) is satisfied,0.03<f1/f2<0.25  (3).
 11. The projection optical system according toclaim 10, wherein Conditional Expression (3-1) is satisfied,0.05<f1/f2<0.22  (3-1).
 12. A projection display device comprising: alight source; a light valve into which light emitted from the lightsource is incident; and the projection optical system according to claim10, wherein the projection optical system projects an optical imageusing modulated light, which is modulated through the light valve, ontoa screen.
 13. A projection optical system consisting of, in order from amagnification side to a reduction side: a first optical system thatconsists of one convex mirror and a plurality of lenses disposed on thereduction side of the convex mirror; and a second optical system thatincludes a plurality of lenses, wherein the second optical system formsan intermediate image at a position conjugate to a reduction sideimaging surface, and the first optical system forms a final image, whichis conjugate to the intermediate image, on a magnification side imagingsurface, wherein a lens closest to the magnification side in the firstoptical system is a negative lens, wherein assuming that a paraxialradius of curvature of the convex mirror is Mr and a focal length of thenegative lens closest to the magnification side in the first opticalsystem is fL1, Conditional Expression (1) is satisfied,0<Mr/fL1<4.5  (1), and wherein assuming that an Abbe number of thesecond lens from the magnification side in the first optical system atthe d line is νd2, Conditional Expression (5) is satisfied,10<νd2<40  (5).
 14. The projection optical system according to claim 13,wherein Conditional Expression (5-1) is satisfied,15<νd2<35  (5-1).
 15. A projection display device comprising: a lightsource; a light valve into which light emitted from the light source isincident; and the projection optical system according to claim 13,wherein the projection optical system projects an optical image usingmodulated light, which is modulated through the light valve, onto ascreen.